The performance of different types of nebulisers: Vulkan direct injection nebuliser (Vulkan DIN), direct injection high efficiency nebuliser (DIHEN), microconcentric nebuliser coupled to cyclonic or double pass spray chamber (MCN-C or MCN-DP, respectively) was investigated and compared when used for sample introduction to ICP-MS or ICP-OES. With ICP-OES, in axial viewing mode, intensity distributions across the radius of the plasma (radial intensity profiles) were determined for different spectral lines with Esum 1.85-15.41 eV to determine fundamental plasma properties for various matrices using Vulkan DIN and MCN-C. The results showed that with the MCN-C the ionisation temperature (Tion) was about the same across the measured region of the plasma (±3.0 mm) whereas with the Vulkan DIN the Tion was significantly lower in the centre of the plasma. A large deviation from local thermodynamic equilibrium, as well as deteriorated stability, was observed for the plasma when using the Vulkan DIN. With ICP-MS noise power spectra (NPS) were generated to identify sources of noise. NPS showed that the magnitude of white noise for the tested sample introduction systems decreased in the following order: Vulkan DIN > DIHEN > MCN-C > MCN-DP. This order follows the decrease of mean droplet size and span of the size distribution, indicating that the white noise is caused by spatial and temporal non-uniform desolvation and ionisation. Another source of noise arose from the peristaltic pump and the magnitude of pump interference noise decreased in the following order: DIHEN > MCN-C/DP > Vulkan DIN. Mains power interference noise and 1/f noise were lower for the direct injection nebulisers compared to the spray chamber systems. The contribution or effects of these noise components on relative standard deviations of steady-state ion-count rate and isotope ratio measurements is discussed in this thesis. Aerosols generated by the Vulkan DIN and the DIHEN were also directly characterised using Particle Dynamic Analysis. The Vulkan DIN produced particles with a mean diameter of ~30 µm and a size distribution between 2-80 µm. With the DIHEN the corresponding values were ~11 µm and 1-40 µm, respectively, with a few particles at 55-78 µm. The mean velocity of particles from the Vulkan DIN was ~10 m s-1 and from the DIHEN ~18 m s-1. The lower velocity allows longer residence time counteracting the effects of the larger droplet size.

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本論文在分析 SP500 指數其中交易最為頻繁的 345 家公司在 1996年各月份的股票數據,市場模式的空間特性已經被證實出來[3][4][5],而我們利用卡忽南 -拉維展開來分解股價對數報酬的時間序列, 利用傅立葉分析,並考慮股價對數報酬是否有時間序列重疊,與比較高頻移動平均對時間序列的影響,藉由參考各股市系統的特徵參數來尋找相似或不同之處。 / We present the results of our analysis of time series for a collection of 345 stocks listed in S&P 500, to show that integrated information on collective fluctuations in financial data can be revealed quantitatively by combined analysis, focusing separately on either the deterministic or the stochastic contents of the system. In comparing the fluctuations of high frequency one-day moving averages (HF1MA) of the original prices of individual stocks with those inherited in the trajectories of Brownian particles [1], also comparing the log return with overlapping time interval with the log return without overlapping time interval, we can quantify the time characteristic properties of the whole system which would direct the motions of tracer particles. In this study, we decompose the fluctuations in Karhunan-Loeve expansions and reveal the system-specific collective properties by analyzing those collective modes in their time-wise as well as the stock-wise bases, obtained for either the original prices or those of HF1MA, and for the log return with or without overlapping time interval.

More than half a decade of X-ray astronomy with various balloon borne and space orbiting X-ray instruments, have led to discoveries and detailed studies of X-ray binaries. An important property of X-ray binaries is intensity variations of different magnitudes in a wide range of timescales from milliseconds (quasi-periodic oscillations, millisecond pulsations), to a few weeks (orbital and super-orbital modulations) or longer (outbursts etc). In this thesis, different types of variabilities of X-ray binaries are considered in X-ray binary population studies and to investigate certain aspects of some individual systems. In Chapter 1, we provide an introduction to various types of variabilities seen in different classes of X-ray binaries. We mention in detail the various periodic and aperiodic variabilities seen in X-ray binaries. In Chapter 2, we describe, in some detail, the various X-ray all sky monitors and X-ray observatories, data from which has been utilized in the work carried out in this thesis. We also describe the various data analysis techniques that we have used. The rest of the thesis is divided into two major sections: Variability studies of indi-vidual systems and X-ray binary population studies Variability studies of individual systems In Chapter 3, we report results from an investigation of energy resolved orbital in-tensity pro les and from exhaustive orbital phase resolved spectroscopic measurements of GX 301{2 with MAXI{GSC . The orbital variation of the spectral parameters, es-pecially the relation between the equivalent width of Fe line and the column density of absorbing matter are then utilized to examine the models for the mode of accretion onto the neutron star in GX 301{2: circumstellar disk model by Pravdo & Ghosh (2001), and the accretion stream model by Leahy & Kostka (2008). A very large equivalent width of the iron line along with a small value of the column density in the orbital phase range 0.10-0.30 after the periastron passage indicates an asymmetry in the distribution of the matter around the neutron star, strongly favoring the accretion stream model by Leahy & Kostka (2008). Presence of an eclipse in an X-ray binary can be useful in determining orbital param-eters like inclination and in estimating the orbital evolution by eclipse timing method, which is reported in Chapter 4. For the HMXB system IGR J16393{4643, we found a short eclipse in the Swift{BAT light-curve and utilized it to constrain the orbital in-clination of the system. We have also studied, for the rst time, broad-band pulsation and spectral characteristic of the system with a Suzaku observation, showing sub-orbital intensity variations. For another eclipsing and non-pulsing HMXB 4U 1700{37, the orbital evolution is studied using mid-eclipse times from observations with narrow eld instruments as well as from long term light-curves of X-ray all sky monitors. The orbital period decay rate is estimated to be 5 10 7 /yr, an order slower than a previous measurement by Rubin et al.(1996). Since no pulsations are detected in this system, it is difficult to estimate its orbital parameters, especially its eccentricity. Using mid-eclipse times from 10 years of Swift{BAT data, we have independently constrained the eccentricity of the binary system. X-ray binary population studies In Chapter 5, we report results from an analysis of the 16 years light-curves of X-ray binaries in 2-10 keV energy band of RXTE{ASM , used to construct the differential and integral probability distributions of count-rates. These distributions are then employed to construct multiple snapshots of X-ray binary luminosity functions of the Milky Way instead of averaging the luminosities, an improvement over previous analysis by Grimm et al. (2002). We found that the averaged luminosities of highly variable X-ray binaries do not represent their true positions in XLFs and the variability of X-ray binaries do indeed signi cantly affect the luminosity functions. In Chapter 6, the measurements of the averaged spectra of X-ray binaries using MAXI{GSC data are reported and are used for constructing the composite X-ray spec-trum. These composite X-ray binary spectra are useful in estimating the contribution of X-ray binaries in extra-galactic SEDs constructed from the simultaneous Chandra / XMM{Newton and NuSTAR observations of these galaxies. These SEDs will also serve as a useful input in estimating the contribution of X-ray binary heating at high redshift IGM during the Epoch of Re-ionization. In Chapter 7, we summarize the main conclusions of the work carried out in this thesis and discuss some future prospects related to this thesis.

El brillo solar varía en escalas de tiempo de minutos a décadas. En particular, la variabilidad fotométrica observada puede relacionarse directamente con el período de rotación. Nuestro conocimiento de este vínculo permite extrapolaciones desde el Sol a otras estrellas. Incluso después de los exitosos estudios estelares logrados por las misiones Kepler o TESS, todavía hay una falta de información en los registros fotométricos de los períodos de rotación de estrellas similares al Sol. Los perfiles de curvas de luz no periódicas, la amplitud de modulación baja (los generados por la aparición aleatoria de características magnéticas y su rápida evolución, en comparación con la escala de tiempo de rotación) son las principales razones poco confiable estimación de la periodicidad en el Sol y sus análogos estelares. Esto indica que las estrellas con un perfil de brillo solar similar también podrían enfrentar un problema de detectabilidad del período de rotación. Lo que implica que solo una fracción de los sistemas similares a los solares se han analizado adecuadamente. Propongo en esta Tesis que una señal clara y optimizada del período de rotación puede ser determinada de manera confiable a partir del perfil del gradiente en el espectro de potencia (GPS) de las series de tiempo de brillo, también denominadas curvas de luz. El GPS es un método novedoso destinado a determinar los períodos de rotación de estrellas como el Sol (es decir, con un perfil de variabilidad de brillo similar). Adicionalmente, el método nos da valiosa información sobre la relación entre fáculas y manchas, lo que, en consecuencia, podría ayudarnos a interpretar la superficie estelar. Este trabajo se basa en el análisis de series de tiempo fotométricas de alta calidad adquiridas por el telescopio Kepler, mediciones de alta estabilidad y alta precisión de la misión SOHO / VIRGO y modelos detallados de variaciones de brillo solar. El método GPS se propone, se desarrolla y prueba con éxito en esta tesis.

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In dieser Arbeit werden mithilfe der Fokker-Planck-Gleichung die Statistiken, vor allem die Leistungsspektren, von Punktprozessen berechnet, die von mehrdimensionalen Integratorneuronen [Engl. integrate-and-fire (IF) neuron], Netzwerken von IF Neuronen und Entscheidungsfindungsmodellen erzeugt werden. Im Gehirn werden Informationen durch Pulszüge von Aktionspotentialen kodiert. IF Neurone mit radikal vereinfachter Erzeugung von Aktionspotentialen haben sich in Studien die auf Pulszeiten fokussiert sind als Standardmodelle etabliert. Eindimensionale IF Modelle können jedoch beobachtetes Pulsverhalten oft nicht beschreiben und müssen dazu erweitert werden. Im erste Teil dieser Arbeit wird eine Theorie zur Berechnung der Pulszugleistungsspektren von stochastischen, multidimensionalen IF Neuronen entwickelt. Ausgehend von der zugehörigen Fokker-Planck-Gleichung werden partiellen Differentialgleichung abgeleitet, deren Lösung sowohl die stationäre Wahrscheinlichkeitsverteilung und Feuerrate, als auch das Pulszugleistungsspektrum beschreibt. Im zweiten Teil wird eine Theorie für große, spärlich verbundene und homogene Netzwerke aus IF Neuronen entwickelt, in der berücksichtigt wird, dass die zeitlichen Korrelationen von Pulszügen selbstkonsistent sind. Neuronale Eingangströme werden durch farbiges Gaußsches Rauschen modelliert, das von einem mehrdimensionalen Ornstein-Uhlenbeck Prozess (OUP) erzeugt wird. Die Koeffizienten des OUP sind vorerst unbekannt und sind als Lösung der Theorie definiert. Um heterogene Netzwerke zu untersuchen, wird eine iterative Methode erweitert. Im dritten Teil wird die Fokker-Planck-Gleichung auf Binärentscheidungen von Diffusionsentscheidungsmodellen [Engl. diffusion-decision models (DDM)] angewendet. Explizite Gleichungen für die Entscheidungszugstatistiken werden für den einfachsten und analytisch lösbaren Fall von der Fokker-Planck-Gleichung hergeleitet. Für nichtliniear Modelle wird die Schwellwertintegrationsmethode erweitert. / This thesis is concerned with the calculation of statistics, in particular the power spectra, of point processes generated by stochastic multidimensional integrate-and-fire (IF) neurons, networks of IF neurons and decision-making models from the corresponding Fokker-Planck equations. In the brain, information is encoded by sequences of action potentials. In studies that focus on spike timing, IF neurons that drastically simplify the spike generation have become the standard model. One-dimensional IF neurons do not suffice to accurately model neural dynamics, however, the extension towards multiple dimensions yields realistic behavior at the price of growing complexity. The first part of this work develops a theory of spike-train power spectra for stochastic, multidimensional IF neurons. From the Fokker-Planck equation, a set of partial differential equations is derived that describes the stationary probability density, the firing rate and the spike-train power spectrum. In the second part of this work, a mean-field theory of large and sparsely connected homogeneous networks of spiking neurons is developed that takes into account the self-consistent temporal correlations of spike trains. Neural input is approximated by colored Gaussian noise generated by a multidimensional Ornstein-Uhlenbeck process of which the coefficients are initially unknown but determined by the self-consistency condition and define the solution of the theory. To explore heterogeneous networks, an iterative scheme is extended to determine the distribution of spectra. In the third part, the Fokker-Planck equation is applied to calculate the statistics of sequences of binary decisions from diffusion-decision models (DDM). For the analytically tractable DDM, the statistics are calculated from the corresponding Fokker-Planck equation. To determine the statistics for nonlinear models, the threshold-integration method is generalized.

This thesis proposes tasks of exercises for mentioned course and design and creation of automated evaluation system for these exercises. This thesis focuses on discussion and exemplary solutions of possible tasks of each exercise and description of created automated evaluation system. For evaluation program are made tests with chosen special data sets, which will prove it’s functionality in general data sets.